Rigging eyes parented to armature offset
The easier and correct way to do it is using the Copy Location object constraint as shown below:



this will fix your problem.

I noticed also that your Pose Position is different from your Rest Position, where the bones are rotated. To make the eyes roll with the bones I added a Copy Rotation as shown below:



This is the end result:

In Rest Position:



In Pose Position:



Updated .blend file can be found here: